An Oseen-type model for swirling internal separated flows

Abstract

The viscous, laminar, separated flow downstream of a sudden expansion in a pipe is studied. The flow is modeled by an Oseen-type equation, but with the additional feature that the nonlinearity in the swirl is retained. Exact solutions are obtained for a high-Reynolds-number limit and for arbitrary Reynolds number by use of an eigenfunction-expansion procedure, in the presence of swirl. This leads to a non-standard eigenvalue problem. When the swirl is sufficiently large, a central recirculating region is observed. The effect of the pressure gradients on the velocity profiles and the central recirculating eddy is discussed. The low-Reynolds-number solutions go over smoothly to the large Reynolds number solution as the Reynolds number increases. Good agreement is obtained with the numerically computed value of the reattachment length.